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Journal of the American Chemical Society Oct 2022The kinetics of chemical reactions are determined by the law of mass action, which has been successfully applied to homogeneous, dilute mixtures. At nondilute...
The kinetics of chemical reactions are determined by the law of mass action, which has been successfully applied to homogeneous, dilute mixtures. At nondilute conditions, interactions among the components can give rise to coexisting phases, which can significantly alter the kinetics of chemical reactions. Here, we derive a theory for chemical reactions in coexisting phases at phase equilibrium. We show that phase equilibrium couples the rates of chemical reactions of components with their diffusive exchanges between the phases. Strikingly, the chemical relaxation kinetics can be represented as a flow along the phase equilibrium line in the phase diagram. A key finding of our theory is that differences in reaction rates between coexisting phases stem solely from phase-dependent reaction rate coefficients. Our theory is key to interpreting how concentration levels of reactive components in condensed phases control chemical reaction rates in synthetic and biological systems.
Topics: Kinetics; Diffusion
PubMed: 36241174
DOI: 10.1021/jacs.2c06265 -
Journal of the Royal Society, Interface Mar 2023How memory shapes animals' movement paths is a topic of growing interest in ecology, with connections to planning for conservation and climate change. Empirical studies...
How memory shapes animals' movement paths is a topic of growing interest in ecology, with connections to planning for conservation and climate change. Empirical studies suggest that memory has both temporal and spatial components, and can include both attractive and aversive elements. Here, we introduce reinforced diffusions (the continuous time counterpart of reinforced random walks) as a modelling framework for understanding the role that memory plays in determining animal movements. This framework includes reinforcement via functions of time before present and of distance away from a current location. Focusing on the interplay between memory and central place attraction (a component of home ranging behaviour), we explore patterns of space usage that result from the reinforced diffusion. Our efforts identify three qualitatively different behaviours: bounded wandering behaviour that does not collapse spatially, collapse to a very small area, and, most intriguingly, convergence to a cycle. Subsequent applications show how reinforced diffusion can create movement trajectories emulating the learning of movement routes by homing pigeons and consolidation of ant travel paths. The mathematically explicit manner with which assumptions about the structure of memory can be stated and subsequently explored provides linkages to biological concepts like an animal's 'immediate surroundings' and memory decay.
Topics: Animals; Ecology; Learning; Diffusion; Movement; Models, Biological
PubMed: 36987616
DOI: 10.1098/rsif.2022.0700 -
Journal of the Royal Society, Interface Mar 2021Swarming has been observed in various biological systems from collective animal movements to immune cells. In the cellular context, swarming is driven by the secretion...
Swarming has been observed in various biological systems from collective animal movements to immune cells. In the cellular context, swarming is driven by the secretion of chemotactic factors. Despite the critical role of chemotactic swarming, few methods to robustly identify and quantify this phenomenon exist. Here, we present a novel method for the analysis of time series of positional data generated from realizations of agent-based processes. We convert the positional data for each individual time point to a function measuring agent aggregation around a given area of interest, hence generating a functional time series. The functional time series, and a more easily visualized of agent aggregation derived from these functions, provide useful information regarding the evolution of the underlying process over time. We extend our method to build upon the modelling of collective motility using drift-diffusion partial differential equations (PDEs). Using a functional linear model, we are able to use the functional time series to estimate the drift and diffusivity terms associated with the underlying PDE. By producing an accurate estimate for the drift coefficient, we can infer the strength and range of attraction or repulsion exerted on agents, as in chemotaxis. Our approach relies solely on using agent positional data. The spatial distribution of diffusing chemokines is not required, nor do individual agents need to be tracked over time. We demonstrate our approach using random walk simulations of chemotaxis and experiments investigating cytotoxic T cells interacting with tumouroids.
Topics: Animals; Cell Tracking; Chemotactic Factors; Chemotaxis; Diffusion; Models, Biological; Movement
PubMed: 33715400
DOI: 10.1098/rsif.2020.0879 -
Journal of Contaminant Hydrology Oct 2021Diffusion coefficients for Na was measured in low-permeability samples (diameter of 3 cm and average length of 7 cm) from the deep disposal site of the Siberian...
Diffusion coefficients for Na was measured in low-permeability samples (diameter of 3 cm and average length of 7 cm) from the deep disposal site of the Siberian Chemical Combine (SCC) using the end-diffusion technique. The direction of diffusion was perpendicular to the direction of bedding. Special equipment was designed and constructed for the experiment. Two types of concentration observations were used. For non-sorbing Na, EC sensors and the length distribution of sorbed elements were used. The synthetic solution used in the experiments was a model of the low-activity contaminant of the SCC and consisted of NaNO (25 g/L) and nitrate compounds of Cs, Ni, Co, and Sr (100 mg/L each). The measured values of the effective diffusion coefficients D for Na from 1.92 × 10 to 1.70 × 10 m/s. The microstructure was studied with X-ray microtomography for the same cores. Image shooting was performed on undisturbed microsamples with a size of 0.91 mm (700 vox). Spatial correlation analysis was performed after the binarization of each obtained 3-D structure. This analysis showed that the spatial correlation scale of the indicator variogram is considerably smaller than the microsample length. Then, a numerical simulation of the Laplace equation with binary coefficients for each microsample was performed. The results were analysed in the form of a plot of the tortuosity versus the porosity. Pore-scale simulations show a nonlinear decrease in the tortuosity with decreasing porosity. Exponential values in the range between 1.8 and 2.4 were found by fitting this graph with Archie's model. Anisotropic tortuosity is also detected in the horizontal and vertical directions. The diffusion coefficients of non-sorbing Na measured in this study agree with those of the pore-scale diffusion simulation of the microtomography data.
Topics: Computer Simulation; Diffusion; Permeability; Porosity; Soil
PubMed: 34298490
DOI: 10.1016/j.jconhyd.2021.103858 -
Biophysical Journal Oct 2021Erk signaling regulates cellular decisions in many biological contexts. Recently, we have reported a series of Erk activity traveling waves that coordinate regeneration...
Erk signaling regulates cellular decisions in many biological contexts. Recently, we have reported a series of Erk activity traveling waves that coordinate regeneration of osteoblast tissue in zebrafish scales. These waves originate from a central source region, propagate as expanding rings, and impart cell growth, thus controlling tissue morphogenesis. Here, we present a minimal reaction-diffusion model for Erk activity waves. The model considers three components: Erk, a diffusible Erk activator, and an Erk inhibitor. Erk stimulates both its activator and inhibitor, forming a positive and negative feedback loop, respectively. Our model shows that this system can be excitable and propagate Erk activity waves. Waves originate from a pulsatile source that is modeled by adding a localized basal production of the activator, which turns the source region from an excitable to an oscillatory state. As Erk activity periodically rises in the source, it can trigger an excitable wave that travels across the entire tissue. Analysis of the model finds that positive feedback controls the properties of the traveling wavefront and that negative feedback controls the duration of Erk activity peak and the period of Erk activity waves. The geometrical properties of the waves facilitate constraints on the effective diffusivity of the activator, indicating that waves are an efficient mechanism to transfer growth factor signaling rapidly across a large tissue.
Topics: Animals; Diffusion; Models, Theoretical; Osteoblasts; Signal Transduction; Zebrafish
PubMed: 34022234
DOI: 10.1016/j.bpj.2021.05.004 -
The Journal of Physical Chemistry. B Apr 2016It has been found in many experiments that the mean square displacement of a Brownian particle x(T) diffusing in a rearranging environment is strictly Fickian, obeying...
It has been found in many experiments that the mean square displacement of a Brownian particle x(T) diffusing in a rearranging environment is strictly Fickian, obeying ⟨(x(T))(2)⟩ ∝ T, but the probability distribution function for the displacement is not Gaussian. An explanation of this is that the diffusivity of the particle itself is changing as a function of time. Models for this diffusing diffusivity have been solved analytically in the limit of small time, but simulations were necessary for intermediate and large times. We show that one of the diffusing diffusivity models is equivalent to Brownian motion in the presence of a sink and introduce a class of models for which it is possible to find analytical solutions. Our solution gives ⟨(x(T))(2)⟩ ∝ T for all times and at short times the probability distribution function of the displacement is exponential which crosses over to a Gaussian in the limit of long times and large displacements.
Topics: Diffusion; Models, Theoretical; Normal Distribution
PubMed: 27029607
DOI: 10.1021/acs.jpcb.6b01527 -
Biophysical Journal Jun 2020Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell...
Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The Fürth equation, the usual characterization of mean-squared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations' MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time- and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer-time cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.
Topics: Cell Movement; Computer Simulation; Diffusion; Models, Biological; Motion
PubMed: 32407685
DOI: 10.1016/j.bpj.2020.04.024 -
ACS Nano Apr 2022Reproducibility of the experimental results and object of study itself is one of the basic principles in science. But what if the object characterized by technologically...
Reproducibility of the experimental results and object of study itself is one of the basic principles in science. But what if the object characterized by technologically important properties is natural and cannot be artificially reproduced one-to-one in the laboratory? The situation becomes even more complicated when we are interested in exploring stochastic properties of a natural system and only a limited set of noisy experimental data is available. In this paper we address these problems by exploring diffusive motion of some natural clays, halloysite and sepiolite, in a liquid environment. By using a combination of dark-field microscopy and machine learning algorithms, a quantitative theoretical characterization of the nanotubes' rotational diffusive dynamics is performed. Scanning the experimental video with the gradient boosting tree method, we can trace time dependence of the diffusion coefficient and probe different regimes of nonequilibrium rotational dynamics that are due to contacts with surfaces and other experimental imperfections. The method we propose is of general nature and can be applied to explore diffusive dynamics of various biological systems in real time.
Topics: Reproducibility of Results; Diffusion; Motion; Machine Learning; Algorithms
PubMed: 35349265
DOI: 10.1021/acsnano.1c11025 -
ACS Nano Sep 2023An important goal for bottom-up synthetic biology is to construct tissue-like structures from artificial cells. The key is the ability to control the assembly of the...
An important goal for bottom-up synthetic biology is to construct tissue-like structures from artificial cells. The key is the ability to control the assembly of the individual artificial cells. Unlike most methods resorting to external fields or sophisticated devices, inspired by the hanging drop method used for culturing spheroids of biological cells, we employ a capillary-driven approach to assemble giant unilamellar vesicles (GUVs)-based protocells into colonized prototissue arrays by means of a coverslip with patterned wettability. By spatially confining and controllably merging a mixed population of lipid-coated double-emulsion droplets that hang on a water/oil interface, an array of synthetic tissue-like constructs can be obtained. Each prototissue module in the array comprises multiple tightly packed droplet compartments where interfacial lipid bilayers are self-assembled at the interfaces both between two neighboring droplets and between the droplet and the external aqueous environment. The number, shape, and composition of the interconnected droplet compartments can be precisely controlled. Each prototissue module functions as a processer, in which fast signal transports of molecules via cell-cell and cell-environment communications have been demonstrated by molecular diffusions and cascade enzyme reactions, exhibiting the ability to be used as biochemical sensing and microreactor arrays. Our work provides a simple yet scalable and programmable method to form arrays of prototissues for synthetic biology, tissue engineering, and high-throughput assays.
Topics: Artificial Cells; Biological Transport; Cell Communication; Diffusion; High-Throughput Screening Assays; Water
PubMed: 37639562
DOI: 10.1021/acsnano.3c03516 -
Soft Matter Oct 2023The lateral diffusion of cell membrane inclusions, such as integral membrane proteins and bound receptors, drives critical biological processes, including the formation...
The lateral diffusion of cell membrane inclusions, such as integral membrane proteins and bound receptors, drives critical biological processes, including the formation of complexes, cell-cell signaling, and membrane trafficking. These diffusive processes are complicated by how concentrated, or "crowded", the inclusions are, which can occupy between 30-50% of the area fraction of the membrane. In this work, we elucidate the effects of increasing concentration of model membrane inclusions in a free-standing artificial cell membrane on inclusion diffusivity and the apparent viscosity of the membrane. By multiple particle tracking of fluorescent microparticles covalently tethered to the bilayer, we show the transition from expected Brownian dynamics, which accurately measure the membrane viscosity, to subdiffusive behavior with decreased diffusion coefficient as the particle area fraction increases from 1% to around 30%, approaching physiological levels of crowding. At high crowding, the onset of non-Gaussian behavior is observed. Using hydrodynamic models relating the 2D diffusion coefficient to the viscosity of a membrane, we determine the apparent viscosity of the bilayer from the particle diffusivity and show an increase in the apparent membrane viscosity with increasing particle area fraction. However, the scaling of this increase is in contrast with the behavior of monolayer inclusion diffusion and bulk suspension rheology. These results demonstrate that physiological levels of model membrane crowding nontrivially alter the dynamics and apparent viscosity of the system, which has implications for understanding membrane protein interactions and particle-membrane transport processes.
Topics: Membranes; Membrane Proteins; Molecular Dynamics Simulation; Biophysical Phenomena; Diffusion; Membranes, Artificial; Viscosity
PubMed: 37791427
DOI: 10.1039/d3sm01269g